Digital SAT Math Practice Questions – Advanced : Systems of two linear equations in two variables

Answer: A

If the system of equations has no solution, then their slopes are equal and \(y\)-intercept are not equal. The lines are parallel.
The slope of the given line is \(-\dfrac{7}{-6}=\dfrac{7}{6}\).
The \(y\)-intercept of the given line is \(\dfrac{-6}{-6}=1\).
The slope of option A is \(-\dfrac{-7}{6}=\dfrac{7}{6}\).
The \(y\)-intercpt of option A is \(0\).
The slope of option B is \(-\dfrac{\dfrac{49}{8}}{\dfrac{-21}{4}}=\dfrac{7}{6}\).
The \(y\)-intercept of option B is \(\dfrac{\dfrac{-21}{4}}{\dfrac{-21}{4}}=1\)
The slope of option C is \(-\dfrac{-14}{\dfrac{-21}{4}}=\dfrac{8}{3}\)
The \(y\)-intercept of option C is \(\0\)
The slope of option D is \(-\dfrac{-7}{6}=\dfrac{7}{6}\)
The \(y\)-intercept of option D is \(\dfrac{6}{6}=1\)